In this paper we introduce a new approach to solve constrained nonlinear programming problems with any desirable accuracy especially when the objective function is a non-smooth one. In this approach for any given desirable accuracy the nonlinear functions of original problem are approximated by a piecewise linear functions. Then we represent an effcient algorithm to find the global solution of the later problem. Also the obtained solution has desirable accuracy. So we may say the error is completely controllable. One of the main advantages of our approach is that the approach can be extended for problems with non-smooth structure by introducing a novel definition of Global Weak Dierentiation in the sense of space. Finally some numerical examples are given to show the efficiency of the proposed approach to solve constraints nonlinear programming problems when the objective function is non-smooth nonlinear functions.

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